Answer:
Step-by-step explanation:
The arc method is basically finding what the a and c coefficients multiply to, and then finding the factors of that that add up to b.
Since we have the quadratic in the ax^2+bx+c form we don't have to adjust anything. Now, a = 8, b = 2 and c = -3. a*c = -24 so now we want to find all the factors of that.
-1 and 24
1 and -24
-2 and 12
2 and -12
-3 and 8
3 and -8
-4 and 6
4 and -6
And after that they repeat. It is important to note that you can use negative on either side, or if a*c was a positive number you could multiply two negatives like 24 can be and 12 as well as -1 and -12.
Now we want to look at all the factor pairs and find one that add together to equal 2 because b = 2. -4 + 6 does it, so there's our choice. Now we can rewrite the original quadratic as 8x^2-4x+6x-3. You can check that this is equivalent by combining like terms It's the same as rewriting it as 8x^2+2x-2-1 because -2 and -1 will combine to get -3. Anyway, now we can factor.
8x^2-4x+6x-3 You can imagine there being two sets of parenthesis.
( 8x^2-4x)+(+6x-3) Now from here we can factor something out of each parenthesis. e can factor out 4x fromt he first and 3 from the second.
4x(2x-1)+3(2x-3) Now, it may not be obvious but you can factor 2x-3 from each term. If that's not clear pretend 2x-3 = u
4xu + 3u Now hopefully it is clear you can factor out this u
u(4x+3) Then we know u = 2x-3 so
(2x-3)(4x+3) And it's factored.
I do want to mention you could have done this with 8x^2+6x-4x-3 with the +6 and -4 switched. I won't go through it here but it may help to do it yourself if you still don't quite understand. Let me know if there is something I can further explain though.
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